Whether roads are designed with bikes in mind impacts it as well. NYC is dense enough for bikes, but much more dangerous to ride one in than most northern European cities.
I'm sure the weather has a lot to do with it as well. If it's icy/snowy a significant portion of the year, that makes it from uncomfortable to dangerous to ride during that time.
NYC might get more snow than Copenhagen, but there is definitely snow here as well, and it doesn't heavily impact bike commuting. The solution is just to clear the bike lanes of snow, and salt to keep them from icing. They have these little machines with rotating brooms that drive down the lanes regularly: http://www.copenhagenize.com/2010/12/ultimate-bike-lane-snow...
Correct. In Barcelona, Spain, when there's risk of snow they use salt. I think the ice isn't the problem, it's the lack of lines who is it. But people is finding that in the end, there's many at least, in Barcelona, to use and they stop using their cars in favor of bikes.